Rewrite as a simplified fraction. ${1.82\overline{7} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1827.7777...\\ 100x &= 182.7777...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1645}$ ${x = \dfrac{1645}{900}} $ ${x = \dfrac{329}{180}} \text{or} {1 \dfrac{149}{180}}$